Method for designing a communication network

ABSTRACT

A method for designing a communication network that can cope with variations in demand pattern is disclosed. Stochastic constraints are generated by using the requested capacity of a demand to produce a stochastic programming problem. Then the stochastic programming problem is converted into an equivalent determinate programming problem on condition of the predetermined probability distribution. The determinate programming problem is solved to determine capacities of the nodes and the links so that the objective function is minimized. This brings about an effect that traffics can be accommodated even if a demand pattern changes to some degree.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to communication network designtechniques, and in particular to a method for designing a communicationnetwork to cope with demand variations and network faults.

2. Description of Related Art

As for a communication network design method conventionally used to copewith demand variations and network faults, there has been proposed amethod of designing path and link capacities for a given specific demandby using linear programming. For example, “Restoration Strategies andSpare Capacity Requirements in Self-Healing ATM Networks,” has beenproposed by Yijun Xiong and Lorne Mason (INFOCOM '97, April 1997). Here,the linear programming refers to a method for handling a problem offinding a maximal or minimal value of a linear objective function under.conditions of linear equalities and inequalities

In a conventional communication network design method, paths ofrespective demands for respective fault states are set so that thecommunication may be maintained even at the time of conceivable linkfault, and the link capacity is designed to be able to accommodate thosepaths at the time of the link fault.

As shown in FIG. 1, as input date, a network topology, a demand, a linkcost coefficient, and conceivable fault states are given. Providing withthe input data, an optimization reference generator 11 generates anobjective function for minimizing the cost concerning the link. A pathaccommodation condition generator 12 generates a constraint formularepresenting that the sum of capacities assigned to path candidates isequal to the requested capacity of the demand.

A link accommodation condition generator 13 generates a constraintformula representing that the capacity of that link is larger than thetotal of capacities of paths passing through each link in each state. Insuccession, an optimization section 14 solves a linear programmingproblem generated by the optimization reference generator 11, the pathaccommodation generator 12, and the link accommodation conditiongenerator 13 to determine the capacities of the paths and links. Ingeneral, a linear programming problem refers to a problem of maximizingor minimizing an objective function represented by a linear equationunder a constraint condition represented by some linear equalities orinequalities.

In the above described conventional communication network design method,there is developed a problem that an optimum design is conducted onlyfor a given determinate demand pattern, where “demand pattern” refers toa set of demands requested between all nodes.

For a given determinate demand pattern, optimization is conducted byusing mathematical programming. Therefore, after ensuring that thedemand pattern can be accommodated, an optimum network minimizing thecost is designed. In other words, there is no assurance for a patterndifferent from that demand pattern.

In actual communication networks, however, the demand pattern differsdepending upon time zone, day of a week, season, and so on, and isvaried by events and the like. Even if the season, the day of week, andthe time zone are the same, it is hardly to be supposed that completelythe same demand pattern is brought about. Furthermore, it is alsopossible that the demand pattern significantly changes according to thewide spread of new communication service or introduction of a newtechnique.

In the conventional network centering on the existing telephone network,forecast of the demand was possible to some degree. In multimedianetworks of recent.years, however, demand forecast has become verydifficult.

SUMMARY OF THE INVENTION

An object of the present invention is to solve the above describedproblems, and to provide a communication network design method that iscapable of accommodating traffic varying due to variations in demandpattern.

According to the present invention, a communication network composed ofa plurality of nodes and links each connecting two nodes is designed bythe following steps: a) inputting network data including a requestedcapacity of a demand as a random variable following a predeterminedprobability distribution between any two nodes and path candidates ofthe demand for accommodating the requested capacity of the demand; b)generating an objective function representing a total cost of the nodesand the links from the network data; c) generating a predetermined setof stochastic constraints by using the requested capacity of the demandto produce a stochastic programming problem including the objectivefunction and the stochastic constraints; d) converting the stochasticprogramming problem into an equivalent determinate programming problemon condition of the predetermined probability distribution; and e)solving the determinate programming problem to determine capacities ofthe nodes and the links so that the objective function is minimized.

The step c) may include the steps of: c-1) generating a stochastic pathaccommodation constraint for causing the requested capacity of thedemand to be accommodated in the path candidates; c-2) generating a linkaccommodation constraint for causing capacities assigned to pathcandidates to be accommodated in the links; and c-3) generating astochastic node accommodation constraint for causing a total ofcapacities of path candidates passing through a node to be accommodatedin the node.

The step c) may include the steps of: c-1) generating a pathaccommodation constraint for causing the requested capacity of thedemand to be accommodated in the path candidates; c-2) generating astochastic link accommodation constraint for causing capacities assignedto path candidates to be accommodated in the links; and c-3) generatinga stochastic node accommodation constraint for causing a total ofcapacities of path candidates passing through a node to be accommodatedin the node.

According to the present invention, the stochastic constraints aregenerated by using the requested capacity of the demand to produce astochastic programming problem and then the stochastic programmingproblem is converted into an equivalent determinate programming problemon condition of the predetermined probability distribution. Thedeterminate programming problem is solved to determine capacities of thenodes and the links so that the objective function is minimized. Thisbrings about an effect that traffics can be accommodated even if ademand pattern changes to some degree. In other words, the stochasticprogramming problem regarding the paths, the links and the nodes isgenerated and then the equivalent determinate programming problem isdetermined. Therefore, traffics can be accommodated even if a demandpattern changes to some degree, resulting in reduced cost for networkconstruction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing the configuration of a conventionalcommunication network design circuit;

FIG. 2 is a block diagram showing the configuration of a communicationnetwork design system for implementing a first embodiment of a networkdesign method according to the present invention;

FIG. 3 is a flow chart showing a network design method according to thefirst embodiment of the present invention;

FIG. 4 is a block diagram showing the configuration of a communicationnetwork design system for implementing the following embodiments of anetwork design method according to the present invention;

FIG. 5 is a flow chart showing a network design method according to asecond embodiment of the present invention;

FIG. 6 is a flow chart showing a network design method according to athird embodiment of the present invention;

FIG. 7 is a flow chart showing a network design method according to afourth embodiment of the present invention;

FIG. 8 is a flow chart showing a network design method according to afifth embodiment of the present invention; and

FIG. 9 is a flow chart showing a network design method according to asixth embodiment of the present invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

First of all, symbols to be used in first to third embodiments accordingto the present invention will be described hereinafter.

l: a link number in the range of 1, . . . , L.

n: a node number in the range of 1, . . . , N.

p: a demand number in the range of 1, . . . , P.

i_(p): a candidate number of a demand p in the range of 1, . . . ,I_(p), where a path candidate i_(p) of a demand p is an arbitrary pathbetween an originating node and a terminating node of a demand p.

ω_(l): a cost coefficient of a link l.

ε: a cost coefficient of a node.

g_(ip/l): an indicator indicating l when a path 1 _(p) of a demand ppasses through a link l (as represented by ip/l) and indicating 0otherwise.

h_(l/n): an indicator indicating l when a link l passes though node n(as represented by l/n) and indicating 0 otherwise.

o_(p/n):an indicator indicating l when a demand p terminates at a node n(as represented by p/n) and indicating 0 otherwise.

λ: the capacity of a unit of link. For example, in a light-wave network,λ represents the number of wavelength paths accommodated in one opticalfiber.

ν: the capacity of a unit of node. For example, in a light-wave network,ν represents the number of wavelength paths accommodated in one opticalcross-connect.

v_(p): requested capacity (random variable) of a demand p.

α: a probability (path accommodation probability) that the requestedcapacity v_(p) of a demand p is assigned to path candidates of thedemand p.

β: a probability (link accommodation probability) that the total ofcapacities of paths i_(p) passing through a link l can be accommodatedin the link l.

γ: a probability (node accommodation probability) that the total ofcapacities of links terminating at a node n and capacities of pathsi_(p) terminating at the node n can be accommodated in the node n.

c_(ip): a capacity (integer variable) assigned to a path candidate i_(p)of a demand p.

r_(ip): a ratio (real number variable) assigned to a path candidatei_(p) when it is assumed that a requested capacity of a demand p is 1.

d_(l): a capacity (integer variable) assigned to a link l.

e_(n): a capacity (integer variable) assigned to a node n.

First Embodiment

Referring to FIG. 2, the communication network design system implementsa first embodiment of the present invention with hardware or software.In the preferred embodiment, a network design procedure according to thefirst embodiment is implemented by a computer running a network designprogram thereon. The network design program according to the firstembodiment is previously stored in a read-only memory (ROM), a magneticstorage, or the like (not shown).

Necessary input data is supplied to an optimization reference generator101, a stochastic path accommodation constraint generator 102, a linkaccommodation constraint generator 103, and a stochastic node constraintgenerator 104. The optimization reference generator 101 produces anobjective function and the other generators 102-104 produce stochasticconstraints to produce a stochastic programming problem. The stochasticprogramming problem is transformed to an equivalent determinateprogramming problem by an equivalent determinate programming problemtransformer 105. An optimization section 106 optimizes the objectivefunction under the equivalent determinate programming problem to producean optimized network design as an output. The details of network designprocedure according to the first embodiment will be describedhereinafter.

Referring to FIG. 3, the system is first provided with a networktopology, demands each having a requested capacity given by probabilitydistribution, path candidates of respective demands, cost coefficientsof link/nodes, path accommodation probabilities, and node accommodationprobabilities (step S301).

On the basis of the above input data, the optimization referencegenerator 101 generates an objective function represented by thefollowing expression (step S302). $\begin{matrix}{{Minimize}\left\lbrack {{\sum\limits_{l - 1}^{L}\quad {\omega_{1}d}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}} \right\rbrack} & (1)\end{matrix}$

The expression (1) means minimization of the cost concerning the linksand the cost concerning the nodes.

The stochastic path accommodation condition generator 102 generates thefollowing constraint expression for paths to accommodate the requestedcapacity of a demand (step S302). $\begin{matrix}{{{Prob}\left\lbrack {{\sum\limits_{i_{p} - 1}^{Ip}\quad c_{ip}} \geq v_{p}} \right\rbrack} \geq {\alpha \quad \left( {{p = 1},\cdots \quad,P} \right)}} & (2)\end{matrix}$

where, Prob [ ] represents the probability that the condition in [ ] issatisfied. The expression (2) represents the accommodation condition ofthe path, and means that the probability that the total of capacitiesassigned to path candidates i_(p) of a demand p exceeds a requestedcapacity v_(p) of the demand p is at least α.

The link accommodation condition generator 103 generates the followingconstraint expression for a link to accommodate capacities assigned topaths (step S303). $\begin{matrix}{{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{i_{p} - 1}^{Ip}\quad {g_{{ip}/1}c_{ip}}}} \leq {\lambda \quad d_{1}\quad \left( {{1 = 1},\cdots \quad,L} \right)}} & (3)\end{matrix}$

The expression (3) means that the capacity d_(l) of a link l exceeds thetotal of capacities of paths i_(p) passing through the link l.

The stochastic node accommodation condition generator 104 generates thefollowing constraint expression for a node to accommodate the capacitiesassigned to paths (step S304). $\begin{matrix}{{{Prob}\left\lbrack {{{\sum\limits_{i = 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p - 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {v\quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}} & (4)\end{matrix}$

 (n=1, . . . , N)  (4)

The expression (4) means that the probability that the capacity of anode n exceeds the termination capacities of the links l and thetermination capacities of the demands p is at least γ.

The expression (1) of the objective function and the constraintexpressions (2), (3) and (4) respectively generated by the optimizationreference generator 101, the stochastic path accommodation constraintgenerator 102, the link accommodation constraint generator 103, and thestochastic node accommodation constraint generator 104 form a stochasticprogramming problem.

The equivalent determinate programming problem transformer 105transforms the stochastic programming problem into an equivalentdeterminate programming problem (step 305). If it is assumed that therequested capacity v_(p) follows a normal distribution having a meanμ_(p) and a variance σ_(p), the expression (2) can be transformed asfollows: $\begin{matrix}{{\overset{Ip}{\sum\limits_{i_{p} - 1}}\quad c_{ip}} \geq {\mu_{p} + {{t(\alpha)}\sigma_{p}\quad \left( {{p = 1},\cdots \quad,P} \right)}}} & (5)\end{matrix}$

where t(α) is a safety coefficient of a standard normal distributionsatisfying α.

In succession, the equivalent determinate programming problemtransformer 105 transforms the expression (4). If it is assumed that thesum total of o_(p/n)v_(p) for p=1, . . . , P follows a normaldistribution having a mean μ_(n) and a variance σ_(p), the mean μ_(n)and the variance σ_(n) are derived by the following expressions (6) and(7), because the requested capacities v_(p) respectively haveindependent distributions. $\begin{matrix}{\mu_{n} = {\sum\limits_{p = 1}^{P}\quad {o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (6)\end{matrix}$

$\begin{matrix}{\left( \sigma_{n} \right)^{2} = {\sum\limits_{p - 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (7)\end{matrix}$

By using the mean μ_(n) and the variance ρ_(n), the expression (4) canbe transformed as follows: $\begin{matrix}{{{{v\quad _{n}} - {\sum\limits_{i = 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}},} & (8)\end{matrix}$

 (n=1, . . . , N)  (8),

where t(γ) is a safety coefficient of a standard normal distributionsatisfying γ.

A linear programming problem obtained by the transformation processingconducted by the equivalent determinate programming problem transformer105 is formed by the expression (1) of the objective function and theconstraint expressions (3), (5), (6), (7) and (8). The optimizationsection 106 solves this linear programming problem, and obtains thecapacities of respective links and the capacities of respective nodes(step S306).

Second Embodiment

Referring to FIG. 4, the communication network design system implementsa second embodiment of the present invention with hardware or software,where symbols to be used in the second embodiment are the same as in thefirst embodiment.

Necessary input data is supplied to an optimization reference generator201, a path accommodation constraint generator 202, a stochastic lintaccommodation constraint generator 203, and a stochastic node constraintgenerator 204. The optimization reference generator 201 produces anobjective function and the other generators 202-204 produce stochasticconstraints to produce a stochastic programming problem. The stochasticprogramming problem is transformed to an equivalent determinateprogramming problem by an equivalent determinate programming problemtransformer 205. An optimization section 206 optimizes the objectivefunction under the equivalent determinate programming problem to producean optimized network design as an output. The details of network designprocedure according to the second embodiment will be describedhereinafter.

Referring to FIG. 5, as input data, the system according to the secondembodiment is first provided with a network topology, demands eachhaving a requested capacity given by probability distribution, pathcandidates of respective demands, cost coefficients of link/nodes, linkaccommodation probabilities, and node accommodation probabilities (stepS501).

On the basis of the provided data, the optimization reference generator201 generates the objective function represented by the followingexpression (step S502): $\begin{matrix}{{{Minimize}\left\lbrack {{\sum\limits_{i - 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}} \right\rbrack}.} & (9)\end{matrix}$

The expression (9) means minimization of the cost concerning the linksand the cost concerning the nodes.

The path accommodation condition generator 202 generates the followingconstraint expression for paths to accommodate the requested capacity ofa demand (step S503). $\begin{matrix}{{\sum\limits_{{ip} - 1}^{Ip}\quad r_{ip}} \geqq {1\quad \left( {{p = 1},\cdots \quad,P} \right)}} & (10)\end{matrix}$

The expression (10) represents the accommodation condition of paths. Theexpression (10) means that the total of ratios of capacities assigned topath candidates i_(p) of the demand p is at least 1 when it is assumedthat the requested capacity is 1.

The stochastic link accommodation condition generator 203 generates thefollowing constraint expression for a link to accommodate the capacitiesassigned to paths (step S504). $\begin{matrix}{{{Prob}\left\lbrack {{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}v_{p}r_{ip}}}} \leq {\lambda \quad d_{1}}} \right\rbrack} \geq {\beta \quad \left( {{1 = 1},\cdots \quad,L} \right)}} & (11)\end{matrix}$

The expression (11) means that the probability that the capacity d_(l)of the link l exceeds the total of capacities of paths i_(p) passingthrough the link l is at least β.

The stochastic node accommodation condition generator 204 generates aconstraint expression for a node to accommodate capacities assigned topaths (step S505). $\begin{matrix}{{{Prob}\left\lbrack {{{\sum\limits_{i - 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p - 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {v\quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}} & (12)\end{matrix}$

 (n=1, . . . , N)  (12)

The expression (12) means that the probability that the capacity of anode n exceeds the termination capacities of the links l and thetermination capacities of the demands p is at least γ.

The expression (9) of the objective function and the constraintexpressions (10), (11) and (12) respectively generated by theoptimization reference generator 201, the path accommodation conditiongenerator 202, the stochastic link accommodation condition generator203, and the stochastic node accommodation condition generator 204 forma stochastic programming problem.

The equivalent determinate programming problem transformer 205transforms this stochastic programming problem into an equivalentdeterminate programming problem (step S506). It is assumed that therequested capacities v_(p) follow mutually independent probabilitydistributions, and each probability distribution has mean μ_(p) and avariance value σ_(p).

If it is assumed that the sum total of g_(lp/l)v_(p)r_(ip) for p=l, . .. , P, i=l, . . . , i_(p) follows probability distribution having a meanμ_(l) and a variance σ_(l), the mean μ_(l) and the variance σ_(l) arederived by the following expressions (13) and (14), because therequested capacities v_(p) are respectively independent. $\begin{matrix}{\mu_{1} = {\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}r_{ip}\mu_{p}\quad \left( {{l = 1},\cdots \quad,L} \right)}}}} & (13) \\{\left( \sigma_{1} \right)^{2} = {\sum\limits_{p - 1}^{p}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {{g_{{ip}/1}\left( r_{ip} \right)}^{2}\left( \sigma_{p} \right)^{2}\quad \left( {{l = 1},\cdots \quad,L} \right)}}}} & (14)\end{matrix}$

 (l=1, . . . , L)  (14)

If it is now assumed that the sum total of g_(lp/l)v_(p)r_(ip) for p=1,. . . , P, i=1, . . . , i_(p) follows a normal distribution, theexpression (11) can be transformed as follows:

λd _(l)≧μ_(l) +t(β)σ_(l)(l=1, . . . , L)  (15)

where t(β) is a safety coefficient of a standard normal distributionsatisfying β.

In succession, the equivalent determinate programming problemtransformer 205 transforms the expression (12). Since the requestedcapacities v_(p) are respectively independent, the mean μ_(n) and thevariance σ_(n) of the sum total of o_(p/n)v_(p) for p=1, . . . , P arederived as follows: $\begin{matrix}{\mu_{n} = {\sum\limits_{p - 1}^{P}\quad {o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (16) \\{\left( \sigma_{n} \right)^{2} = {\sum\limits_{p - 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (17)\end{matrix}$

If it is assumed that the sum total of g_(ip/l)v_(p) for p=1, . . . , Pfollows a normal distribution, the expression (12) can be transformed asfollows: $\begin{matrix}{{{v\quad e_{n}} - {\overset{L}{\sum\limits_{l - 1}}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (18)\end{matrix}$

 (n=1,. . . , N)  (18)

where t(γ) is a safety coefficient of standard normal distributionsatisfying γ.

A linear programming problem obtained by the transformation processingconducted by the equivalent determinate programming problem transformer205 is formed by the expression (9) of the objective function and theconstraint expressions (10), (13), (14), (15), (16), (17) and (18). Theoptimization means 206 solves this linear programming problem, andobtains the capacities of respective links and the capacity of the node(step S507).

Third Embodiment

Referring to FIG. 6, the communication network design system implementsa third embodiment of the present invention with hardware or software,where symbols to be used in the third embodiment are the same as in thefirst embodiment except that c_(ip) is a capacity [variable of astochastic programming problem (random variable)] assigned to a pathcandidate i_(p) for the requested capacity of a demand p. The basicconfiguration of the system for implementing the third embodiment is thesame as in the second embodiment as shown in FIG. 4.

As input data, the system according to the third embodiment is firstprovided with a network topology, demands each having a requestedcapacity given by probability distribution, path candidates ofrespective demands, cost coefficients of link/nodes, link accommodationprobabilities, and node accommodation probabilities (step S601).

On the basis of the provided data, the optimization reference generator201 generates the objective function represented by the followingexpression (step S602): $\begin{matrix}{{{Minimize}\left\lbrack {{\sum\limits_{i - 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}} \right\rbrack}.} & (19)\end{matrix}$

The expression (19) means minimization of the cost concerning the linksand the cost concerning the nodes.

The path accommodation condition generator 202 generates the followingconstraint expression for paths to accommodate the requested capacity ofa demand (step S603): $\begin{matrix}{{{\sum\limits_{{ip} - 1}^{Ip}\quad c_{ip}} \geqq {v_{p}\quad \left( {{p = 1},\cdots \quad,P} \right)}},} & (20)\end{matrix}$

where c_(ip) is a capacity (a variable of a stochastic programmingproblem or a random variable] assigned to a path candidate i_(p) for therequested capacity of a demand p.

The expression (20) represents the accommodation condition of paths. Theexpression (20) means that the total of capacities assigned to pathcandidates i_(p) of the demand p is at least the requested capacityv_(p) of the demand p.

The stochastic link accommodation condition generator 203 generates thefollowing constraint expression for a link to accommodate the capacitiesassigned to paths (step S604). $\begin{matrix}{{{Prob}\left\lbrack {{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}c_{ip}}}} \leq {\lambda \quad d_{1}}} \right\rbrack} \geq {\beta \quad \left( {{1 = 1},\cdots \quad,L} \right)}} & (21)\end{matrix}$

 (l=1, . . . , L)  (21)

The expression (21) means that the probability that the capacity d_(l)of the link l exceeds the total of capacities of paths i_(p) passingthrough the link l is at least β.

The stochastic node accommodation condition generator 14 generates thefollowing constraint expression for a node to accommodate capacitiesassigned to paths (step S605). $\begin{matrix}{{{Prob}\left\lbrack {{{\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p = 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {v\quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}} & (22)\end{matrix}$

 (n=1, . . . , N)  (22)

The expression (22) means that the probability that the capacity of anode n exceeds the termination capacities of the links l and thetermination capacities of the demands p is at least γ.

The expression (19) of the objective function and the constraintexpressions (20), (21) and (22) respectively generated by theoptimization reference generator 201, the path accommodation conditiongenerator 202, the stochastic link accommodation condition generator203, and the stochastic node accommodation condition generator 204 forma stochastic programming problem.

The equivalent determinate programming problem transformer 205transforms this stochastic programming problem into an equivalentdeterminate programming problem (step S606). If it is assumed that therequested capacities v_(p) follow mutually independent probabilitydistributions each having mean μ_(p) and a variance σ_(p), the meanμ_(ip) and the variance σ_(ip) of a random variable c_(ip) can berepresented as follows: $\begin{matrix}{{\sum\limits_{{ip} - 1}^{Ip}\quad \mu_{ip}} = {\mu_{p}\quad \left( {{p = 1},\cdots \quad,P} \right)}} & (23)\end{matrix}$

$\begin{matrix}{{\sum\limits_{{ip} - 1}^{Ip}\quad \left( \sigma_{ip} \right)^{2}} = {\left( \sigma_{p} \right)^{2}\quad \left( {{p = 1},\cdots \quad,P} \right)}} & (24)\end{matrix}$

In succession, the equivalent determinate programming problemtransformer 205 transforms the expression (21). If it is assumed thatthe random variables c_(ip) are mutually independent, the mean μ_(l) andthe variance σ_(l) of the sum total of g_(ip/l)c_(ip), p=1, . . . , P,i_(p)=1, . . . , I_(p) are derived as follows: $\begin{matrix}{\mu_{1} = {\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} = 1}^{Ip}\quad {g_{{ip}/1}\mu_{ip}\quad \left( {{l = 1},\cdots \quad,L} \right)}}}} & (25) \\{\left( \sigma_{1} \right)^{2} = {\sum\limits_{p = 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {{g_{{ip}/1}\left( \sigma_{ip} \right)}^{2}\quad \left( {{l = 1},\cdots \quad,L} \right)}}}} & (26)\end{matrix}$

If it is assumed that the sum total of g_(ip)/lcip, p=1, . . . , P,i_(p)=1, . . . , I_(p) follows normal distribution, the expression (21)can be transformed as follows:

λd _(i)≧μ_(l) +t(β)σ_(l)(l=1, . . . , L)  (27)

where t(β) is a safety coefficient of standard normal distributionsatisfying β.

If it is assumed that the sum total of o_(p/n)v_(p)p=l, . . . , Pfollows a normal distribution and each of the requested capacities v_(p)has independent distribution, the mean μ_(n) and the variance σ_(n)become as follows: $\begin{matrix}{\mu_{n} = {\sum\limits_{p - 1}^{P}\quad {{o_{p/n}\left( \sigma_{n} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (28) \\{\left( \sigma_{n} \right)^{2} = {\sum\limits_{p - 1}^{P}\quad {{o_{p/n}\left( \sigma_{n} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (29)\end{matrix}$

By using the mean μ_(n) and the variance σ_(n), the expression (22) canbe transformed as follows; $\begin{matrix}{{{v\quad e_{n}} - {\sum\limits_{l = 1}^{L}\quad h_{l/n}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (30)\end{matrix}$

where t(γ) is a safety coefficient of standard normal distributionsatisfying γ.

A nonlinear programming problem obtained by the transformationprocessing conducted by the equivalent determinate programming problemtransformer 205 is formed by the expression (19) of the objectivefunction and the constraint expressions (23), (24), (25), (26), (27),(28), (29) and (30). The optimization means 206 solves this nonlinearprogramming problem, and obtains the capacities of respective links andthe capacity of the node (step S607).

Fourth Embodiment

First of all, symbols to be used in fourth to sixth embodimentsaccording to the present invention will be described hereinafter.

l: a link number in the range of 1, . . . , L.

n: a node number in the range of 1, . . . , N.

p: a demand number in the range of 1, . . . , P.

s: a network state in the range of 0, . . . , S, where 0 represents anormal state where no fault occurs, and each of 1, . . . , S representsa fault state in which there is a fault on some link.

i_(p): a path candidate number in a demand p in the range of 1, . . . ,I_(p), where a path candidate i_(p) of the demand p is an arbitrary pathbetween an originating node and a terminating node of the demand p, andis provided as an input.

ω_(l): a cost efficient of a link l.

ε: a cost efficient of a node.

g_(ip/l): an indicator indicating l when a path i_(p) of a demand ppasses through a link l (as represented by i_(p/l)) and indicating 0otherwise.

h_(l/n): an indicator indicating l when a link l passes through a node n(as represented by l/n) and indicating 0 otherwise.

o_(p/n): an indicator indicating l when a demand p terminates at a noden (as represented by p/n), and indicating 0 otherwise.

λ: a capacity of a unit of link. For example, in a light-wave network, λrepresents the number of wavelength paths accommodated by one opticalfiber.

ν: a capacity of a unit of node. For example, in a light-wave network, νrepresents the number of wavelength paths accommodated by one opticalcross-connect.

v_(p): a requested capacity of a demand p indicating a random variablehaving mean μ_(p) and a variance σ_(p).

f_(l/a): an indicator indicating 0 when a link l is faulty, andindicating 1 when the link l is normal. In the normal state representedas s=0, f_(l/a)=1 in every link l.

α: a probability (path accommodation probability) that a requestedcapacity v_(p) of a demand p is assigned to path candidates of thedemand p.

β: a probability (link accommodation probability) that the total ofcapacities of paths i_(p) passing through a link l can be accommodatedby the link l.

γ: a probability (node accommodation probability) that the total ofcapacities of links terminating at a node n and a capacity of pathsi_(p) terminating at the node n can be accommodated in the node n.

c_(ipa): capacity (integer variable) assigned to a path i_(p) of ademand p in a state s.

r_(ipε): a ratio (real number variable) assigned to a path candidatei_(p) when it is assumed that a requested capacity of a demand p is 1.

d_(l): a capacity (integer variable) assigned to a link l.

e_(n): a capacity (integer variable) assigned to a node n.

Referring to FIG. 7, the communication network design system implementsa fourth embodiment of the present invention with hardware or software.In the preferred embodiment, a network design procedure according to thefirst embodiment is implemented by a computer running a network designprogram thereon. The network design program according to the firstembodiment is previously stored in a read-only memory (ROM), a magneticstorage, or the like (not shown) The basic configuration of the systemfor implementing the fourth embodiment is the same as in the firstembodiment as shown in FIG. 2.

As input data, the system is first provided with a network topology,demands each having a requested capacity given by probabilitydistribution, path candidates of the respective demands, costcoefficients of link/nodes, link accommodation probabilities, nodeaccommodation probabilities, and a conceivable fault scenario (stepS701). Here, the fault scenario is a set of fault scenarios in the casewhere a set of simultaneously occurring link faults is defined as onefault scenario.

On the basis of the provided data, the optimization reference generator101 generates the objective function represented by the followingexpression (step S702): $\begin{matrix}{{Minimize}\left\lbrack {{\sum\limits_{l - 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}} \right\rbrack} & (31)\end{matrix}$

The expression (31) means minimization of the cost concerning the linksand the cost concerning the nodes.

The stochastic path accommodation condition generator 102 generates thefollowing constraint expression for paths to accommodate the requestedcapacity of a demand (step S702). $\begin{matrix}{{{Prob}\left\lbrack {{\sum\limits_{{ip} - 1}^{Ip}\quad c_{ips}} \leq v_{p}} \right\rbrack} \geq {\alpha \quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}} & (32)\end{matrix}$

 (p=1, . . . , P, s=0, . . . ,S)  (32)

The expression (32) means that the probability that the total ofcapacities assigned to path candidates i_(p) of a demand p exceeds arequested capacity v_(p) of the demand p in the state s is at least α.

The link accommodation condition generator 103 generates the followingconstraint expression for a link to accommodate capacities assigned topaths (step S704). $\begin{matrix}{{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}c_{{ip}\quad ɛ}}}} \leq {\lambda \quad d_{1}\quad \left( {{l = 1},\cdots \quad,L,{s = 0},\cdots \quad,S} \right)}} & (33)\end{matrix}$

 (1=l, . . . , L, s=0, . . . , S)  (33)

The expression (33) means that the capacity d_(l) of a link l exceedsthe total of capacities of paths i_(p) passing through the link l in astate s.

The stochastic node accommodation condition generator 104 generates thefollowing constraint expression for a node to accommodate the capacitiesassigned to paths (step S705). $\begin{matrix}{{{Prob}\left\lbrack {{{\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p = 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {v\quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}} & (34)\end{matrix}$

 (n=1, . . . , N)  (34)

The expression (34) means that the probability that the capacity of anode n exceeds the termination capacities of the links l and thetermination capacities of the demands p is at least γ.

The expression (31) of the objective function and the constraintexpressions (32), (33) and (34) respectively generated by theoptimization reference generator 101, the stochastic path accommodationconstraint generator 102, the link accommodation constraint generator103, and the stochastic node accommodation constraint generator 104 forma stochastic programming problem.

The equivalent determinate programming problem transformer 105transforms this stochastic programming problem into an equivalentdeterminate programming problem (step S706). If it is assumed that therequested capacities v_(p) follow normal distributions each of which hasmean μ_(p) and variance σ_(p) and which are mutually independent, theexpression (32) can be transformed as follows: $\begin{matrix}{{\sum\limits_{{ip} = 1}^{Ip}\quad c_{{ip}\quad e}} \geq {\mu_{p} + {{t(\alpha)}\sigma_{p}\quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}}} & (35)\end{matrix}$

 (p=1, . . . , P, s=0, . . . , S)  (35)

where t(α) is a safety coefficient of standard normal distributionsatisfying α.

In succession, the equivalent determinate programming problemtransformer 105 transforms the expression (34). If it is assumed thatthe sum total of o_(p/n)v_(p) for p=1, . . . , P follows a normaldistribution having mean μ_(n) and variance σ_(n) and each of therequested capacities v_(p) has independent distribution, the mean μ_(n)and the variance σ_(n) are derived as follows: $\begin{matrix}{\mu_{n} = {\sum\limits_{p - 1}^{P}\quad {o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (36) \\{\left( \sigma_{n} \right)^{2} = {\sum\limits_{p = 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (37)\end{matrix}$

By using the mean μ_(n) and the variance σ_(n), the expression (34) canbe transformed as follows: $\begin{matrix}{{{v\quad e_{n}} - {\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (38)\end{matrix}$

 (n=1, . . . , N)  (37)

where t(γ) is a safety coefficient of standard normal distributionsatisfying γ.

A linear programming problem obtained by the transformation processingconducted by the equivalent determinate programming problem transformer109 is formed by the expression (31) of the objective function and theconstraint expressions (33), (35), (36), (37) and (38). The optimizationmeans 106 solves this linear programming problem, and obtains thecapacities of respective links and the capacity of the node (step S707).

Fifth Embodiment

The communication network design system implements a fifth embodiment ofthe present invention with hardware or software. In the preferredembodiment, a network design procedure according to the fifth embodimentis implemented by a computer running a network design program thereon.The network design program according to the fifth embodiment ispreviously stored in a read-only memory (ROM), a magnetic storage, orthe like (not shown). The basic configuration of the system forimplementing the fifth embodiment is the same as in the secondembodiment as shown in FIG. 4. The network design method according tothe fifth embodiment is capable of coping with link faults in the secondembodiment. Symbols to be used in the fifth embodiment are the same asin the fourth embodiment.

Referring to FIG. 8, as input data, the system is first provided with anetwork topology, demands each having a requested capacity given byprobability distribution, path candidates of respective demands, costcoefficients of link/nodes, link accommodation probabilities, nodeaccommodation probabilities, and conceivable faults (step S801).

On the basis of the provided data, the optimization reference generator201 generates the objective function represented by the followingexpression (step S801): $\begin{matrix}{{Minimize}\left\lbrack {{\sum\limits_{l = 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n = 1}^{N}\quad e_{n}}}} \right\rbrack} & (39)\end{matrix}$

The expression (39) means minimization of the cost concerning the linksand the cost concerning the nodes.

The path accommodation condition generator 202 generates the followingconstraint expression for paths to accommodate the requested capacity ofa demand (step S802). $\begin{matrix}{{\sum\limits_{{ip} = 1}^{Ip}\quad r_{{ip}\quad e}} \geqq \quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)} & (40)\end{matrix}$

The expression (40) represents the accommodation condition of paths. Theexpression (40) means that the total of capacities assigned to pathcandidates i_(p) of the demand p is at least 1 with respect to therequested capacity.

The stochastic link accommodation condition generator 203 generates thefollowing constraint expression for a link to accommodate the capacitiesassigned to paths (step S804). $\begin{matrix}{{{Prob}\left\lbrack {{\sum\limits_{p = 1}^{P}\quad {\sum\limits_{{ip} = 1}^{Ip}\quad {g_{{ip}/1}v_{p}r_{{ip}\quad ɛ}}}} \leq {f_{1/ɛ}\lambda \quad d_{1}}} \right\rbrack} \geqq {\beta \quad \left( {{l = 1},\cdots \quad,L,{s = 0},\cdots \quad,S} \right)}} & (41)\end{matrix}$

 (l=1, . . . , L, s=0, . . . , S)  (41)

The expression (41) means that the probability that the capacity d_(l)of the link l exceeds the total of capacities of paths i_(p) passingthrough the link l in the state s is at least β.

The stochastic node accommodation condition generator 204 generates thefollowing constraint expression for a node to accommodate capacitiesassigned to paths (step S805). $\begin{matrix}{{{Prob}\left\lbrack {{{\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p - 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {v\quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}} & (42)\end{matrix}$

 (n=1, . . . , N)  (42)

The expression (42) means that the probability that the capacity of anode n exceeds the termination capacities of the links l and thetermination capacities of the demands p is at least γ.

The expression (39) of the objective function and the constraintexpressions (40), (41) and (42) respectively generated by theoptimization reference generator 201, the path accommodation conditiongenerator 202, the stochastic link accommodation condition generator203, and the stochastic node accommodation condition generator 204 forma stochastic programming problem.

The equivalent determinate programming problem transformer 205transforms this stochastic programming problem into an equivalentdeterminate programming problem (step S806). If it is assumed that therequested capacities v_(p) follow mutually independent normaldistributions each having mean μ_(p) and variance σ_(p), then the meanμ_(l) and the variance σ_(l) of the sum total of g_(ip/l)v_(p)r_(ipa)for p=1, . . . , P, i_(p)=1, . . . , I_(p) can be derived as follows:$\begin{matrix}{\mu_{1} = {\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}r_{{ip}\quad e}\mu_{p}\quad \left( {{l = 1},\cdots \quad,L} \right)}}}} & (43) \\{\left( \sigma_{1} \right)^{2} = {\sum\limits_{p = 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {{g_{{ip}/1}\left( r_{{ip}\quad ɛ} \right)}^{2}\left( \sigma_{p} \right)^{2}\quad \left( {{l = 1},\cdots \quad,L} \right)}}}} & (44)\end{matrix}$

 (l=1, . . . , L)  (44)

If it is now assumed that the sum total of g_(ip/l)v_(p)r_(ipε) for p=1,. . . , P, i=1, . . . , I_(p) follows a normal distribution, theexpression (41) can be transformed as follows:

λd _(l)≧μ_(l) +t(β)σ_(l) (l=1, . . . , L)  (45)

where t(β) is a safety coefficient of standard normal distributionsatisfying β.

In succession, the equivalent determinate programming problemtransformer 205 transforms the expression (42). Since the requestedcapacities v_(p) are respectively independent, the mean μ_(n) and thevariance σ_(n) of the sum total of o_(p/n)v_(p) for p=1, . . . , Pderived as follows: $\begin{matrix}{\mu_{n} = {\sum\limits_{p - 1}^{P}\quad {o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (46) \\{\left( \sigma_{n} \right)^{2} = {\sum\limits_{p - 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (47)\end{matrix}$

If it is assumed that the sum total of o_(p/n)v_(p) for p=1, . . . , Pfollows a normal distribution, the expression (52) can be transformed asfollows: $\begin{matrix}{{{v\quad e_{n}} - {\sum\limits_{l - 1}^{L}\quad h_{l/n}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (48)\end{matrix}$

where t(γ) is a safety coefficient of standard normal distributionsatisfying γ.

A nonlinear programming problem obtained by the transformationprocessing conducted by the equivalent determinate programming problemtransformer 205 is formed by the expression (39) of the objectivefunction and the constraint expressions (40), (43), (44), (45), (46),(47) and (48). The optimization section 206 solves this nonlinearprogramming problem, and obtains the capacities of respective links andthe capacity of the node (step S807).

Sixth Embodiment

The communication network design system implements a sixth embodiment ofthe present invention with hardware or software. In the preferredembodiment, a network design procedure according to the sixth embodimentis implemented by a computer running a network design program thereon.The network design program according to the sixth embodiment ispreviously stored in a read-only memory (ROM), a magnetic storage, orthe like (not shown). The basic configuration of the system forimplementing the sixth embodiment is the same as in the secondembodiment as shown in FIG. 4. The network design method according tothe sixth embodiment is capable of coping with link faults in the secondembodiment. Symbols to be used in the sixth embodiment are the same asin the fourth embodiment except that c_(ipε) is a capacity [variable ofa stochastic programming problem (random variable)] assigned to a pathi_(p) in a state s with respect to a requested capacity of a demand p.

Referring to FIG. 9, as input data, the system is first provided with anetwork topology, demands each having a requested capacity given byprobability distribution, path candidates of the respective demands,cost coefficients of link/nodes, link accommodation probabilities, nodeaccommodation probabilities, and conceivable faults (step S901).

On the basis of the input data, the optimization reference generator 201generates the objective function represented by the following expression(step S902): $\begin{matrix}{{Minimize}\left\lbrack {{\sum\limits_{l = 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}} \right\rbrack} & (49)\end{matrix}$

The expression (49) means minimization of the cost concerning the linksand the cost concerning the nodes.

The path accommodation condition generator 202 generates the followingconstraint expression for paths to accommodate the requested capacity ofa demand (step S903). $\begin{matrix}{{\sum\limits_{{ip} = 1}^{Ip}\quad c_{{ip}\quad ɛ}} \geq {v_{p}\quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}} & (50)\end{matrix}$

The expression (50) represents the accommodation condition of paths. Theexpression (50) means that the total of capacities assigned to pathcandidates i_(p) of the demand p in the state s is at least therequested capacity v_(p) of the demand p.

The stochastic link accommodation condition generator 203 generates thefollowing constraint expression for a link to accommodate the capacitiesassigned to paths (step S904). $\begin{matrix}{{{Prob}\left\lbrack {{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}c_{ips}}}} \leq {\lambda \quad f_{l/s}_{1}}} \right\rbrack} \geq {\beta \quad \left( {{l = 1},\cdots \quad,L,{s = 0},\cdots \quad,S} \right)}} & (51)\end{matrix}$

 (l=1, . . . , L, s=0, . . . , S)  (51)

The expression (51) means that the probability that the capacity d_(l)of the link l exceeds the total of capacities of paths i_(p) passingthrough the link l in the state s is at least β.

The stochastic node accommodation condition generator 204 generates thefollowing constraint expression for a node to accommodate capacitiesassigned to paths (step S905). $\begin{matrix}{{{Prob}\left\lbrack {{{\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p = 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {v\quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}} & (52)\end{matrix}$

The expression (52) means that the probability that the capacity of anode n exceeds the termination capacities of the links l and thetermination capacities of the demands p is at least γ.

The expression (49) of the objective function and the constraintexpressions (50), (51) and (52) respectively generated by theoptimization reference generator 201, the path accommodation conditiongenerator 202, the stochastic link accommodation condition generator203, and the stochastic node accommodation condition generator 204 forma stochastic programming problem.

The equivalent determinate programming problem transformer 205transforms this stochastic programming problem into an equivalentdeterminate programming problem (step S906). If it is assumed that therequested capacities v_(p) follow mutually independent normaldistributions each having mean μ_(p) and variance σ_(p), then the meanμ_(ips) and the variance σ_(ips) of the random variable c_(ips) can bederived as follows: $\begin{matrix}{{\sum\limits_{{ip} - 1}^{Ip}\quad \mu_{{ip}\quad ɛ}} \leq {\mu_{p}\quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}} & (53) \\{{\sum\limits_{{ip} - 1}^{Ip}\quad \left( \sigma_{{ip}\quad ɛ} \right)^{2}} = {\left( \sigma_{p} \right)^{2}\quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}} & (54)\end{matrix}$

 (p=1, . . . , P, s=0, . . . , S)  (54)

In succession, the equivalent determinate programming problemtransformer 205 transforms the expression (51). If it is assumed thatthe random variables c_(ips) have mutually independent distributions,the mean value μ_(la) and the variance value σ_(ls) of the sum total ofg_(ip/l)c_(ips) for p=1, . . . , P, i_(p) =1, . . . , I _(p) can bederived as follows: $\begin{matrix}{\mu_{ls} = {\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}\mu_{{ip}\quad ɛ}\quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}}}} & (55)\end{matrix}$

$\begin{matrix}{\left( \sigma_{1\quad ɛ} \right)^{2} = {\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} = 1}^{Ip}\quad {{g_{{ip}/1}\left( \sigma_{{ip}\quad ɛ} \right)}^{2}\quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}}}} & (56)\end{matrix}$

 (p=1, . . . , P, s=0, . . . , S)  (56)

If it is assumed that the sum total of g_(ip)c_(ips) for p=1, . . . , P,i_(p)=1, . . . , I_(p) follows a normal distribution, the expression(51) can be transformed as follows:

λf _(l/s)≧μ_(ls) +t(β)σ_(ls) (l=1, . . . , L, s=0, . . . , S)  (57)

where t(β) is a safety coefficient of standard normal distributionsatisfying β.

Furthermore, If it is now assumed that each of the requested capacitiesv_(p) has an independent distribution, the mean value μ_(p) and thevariance σ_(n) of the sum total of o_(p/n)v_(p) for p=1, . . . , P arederived as follows: $\begin{matrix}{\mu_{n} = {\sum\limits_{p - 1}^{P}\quad {o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (58) \\{\left( \sigma_{n} \right)^{2} = {\sum\limits_{p - 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (59)\end{matrix}$

If it is assumed that the sum total of o_(p/n)v_(p) for p=1, . . . Pfollows a normal distribution, the expression (52) can be transformed asfollows: $\begin{matrix}{{{v\quad e_{n}} - {\sum\limits_{l - 1}^{L}\quad h_{l/n}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}} & (60)\end{matrix}$

where t(γ) is a safety coefficient of standard normal distributionsatisfying γ.

A nonlinear programming problem obtained by the transformationprocessing conducted by the equivalent determinate programming problemtransformer 205 is formed by the expression (49) of the objectivefunction and the constraint expressions (53), (54), (55), (56), (57),(58), (59) and (60). The optimization means 206 solves this nonlinearprogramming problem, and obtains the capacities of respective links andthe capacity of the node (step S907).

As described above, such a stochastic programming problem as to minimizethe cost under given stochastic accommodation conditions concerningcapacities of paths, links and nodes is set by the optimizationreference generator 101 or 201, the stochastic pass accommodationconstraint generator 102 or the path accommodation condition generator202, the link accommodation condition generator 103 or the stochasticlink accommodation condition generator 203, and the stochastic nodeaccommodation constraint generator 104 or the stochastic nodeaccommodation condition generator 204. This stochastic programmingproblem is transformed to an equivalent determinate programming problemby the equivalent determinate programming problem transformer 105 or205. The equivalent determinate programming problem is solved by theoptimization section 106 or 206. As a result, it is possible to design anetwork which can accommodate traffics even if the traffic patternchanges to some degree and which can be constructed at a low cost.

As described above, according to the present invention a predeterminedset of stochastic constraints are generated by using the requestedcapacity of the demand to produce a stochastic programming problem andthen the stochastic programming problem is converted into an equivalentdeterminate programming problem on condition of the predeterminedprobability distribution. The determinate programming problem is solvedto determine capacities of the nodes and the links so that the objectivefunction is minimized. This brings about an effect that the traffics canbe accommodated even if a demand pattern changes to some degree.

What is claimed is:
 1. A method for designing a communication networkcomposed of a plurality of nodes and links each connecting two nodes,comprising the steps of: a) inputting network data including a requestedcapacity of a demand as a random variable following a predeterminedprobability distribution between any two nodes and path candidates ofthe demand for accommodating the requested capacity of the demand: b)generating an objective function representing a total cost of the nodesand the links from the network data; c) generating a predetermined setof stochastic constraints by using the requested capacity of the demandto produce a stochastic programming problem including the objectivefunction and the stochastic constraints; d) converting the stochasticprogramming problem into an equivalent determinate programming problemon condition of the predetermined probability distribution: and e)solving the determinate programming problem to determine capacities ofthe nodes and the links so that the objective function is minimized. 2.The method according to claim 1, wherein the step c) comprises the stepsof: c-1) generating a stochastic path accommodation constraint forcausing the requested capacity of the demand to be accommodated in thepath candidates; c-2) generating a link accommodation constraint forcausing capacities assigned to path candidates to be accommodated in thelinks; and c-3) generating a stochastic node accommodation constraintfor causing a total of capacities of path candidates passing through anode to be accommodated in the node.
 3. The method according to claim 2,wherein, in the step c-1), the stochastic path accommodation constraintcauses a probability that a total of capacities assigned to pathcandidates of a demand is not smaller than the requested capacity of thedemand to be at least a predetermined path accommodation probability, inthe step c-2), the link accommodation constraint causes a total ofcapacities of path candidates passing through a link to be accommodatedin the link, and in the step c-3), the stochastic node accommodationconstraint causes a probability that a capacity assigned to a nodeexceeds a total of termination capacity of a link and terminationcapacity of the demand to be at least a predetermined node accommodationprobability.
 4. The method according to claim 3, wherein the stochasticpath accommodation constraint generated in the step c-1) is representedby:${{{Prob}\left\lbrack {{\sum\limits_{i_{p} = 1}^{Ip}\quad c_{ip}} \geq v_{p}} \right\rbrack} \geq {\alpha \quad \left( {{p = 1},\cdots \quad,P} \right)}},$

where Prob [ ] represents a probability that the condition in [ ] issatisfied, p is a demand number, i_(p) is a candidate number of a demandp in the range of 1, . . . , I_(p) where a path candidate i_(p) of ademand p is an arbitrary path between an originating node and aterminating node of a demand p, c_(ip) is a capacity (integer variable)assigned to a path candidate i_(p) of a demand p, v_(p) is a requestedcapacity (random variable) of a demand p, and α is a probability (pathaccommodation probability) that the requested capacity v_(p) of a demandp is assigned to path candidates of the demand p; the link accommodationconstraint generated by the step c-2) is represented by:${\sum\limits_{p - 1}^{P}\quad {{\sum\limits_{i}}_{p - 1}^{Ip}\quad {g_{{ip}/1}c_{ip}}}} \leq {\lambda \quad d_{1}\quad \left( {{l = 1},\cdots \quad,L} \right)}$

where l: is a link number, g_(ip/l) is an indicator indicating l when apath candidate i_(p) of a demand p passes through a link l (asrepresented by ip/l) and indicating 0 otherwise, d_(l) is a capacity(integer variable) assigned to a link l, and λ is a capacity of a link,and the stochastic node accommodation constraint generated by the stepc-3) is represented by:${{{Prob}\left\lbrack {{{\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p = 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {v\quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}},$

 (n=1, . . . , N) where n is a node number, h_(l/n) is an indicatorindicating l when a link l passes though node n (as represented by l/n)and indicating 0 otherwise, o_(p/n) is an indicator indicating l when ademand p terminates at a node n (as represented by p/n) and indicating 0otherwise, ν is a capacity of a node, e_(n) is a capacity (integervariable) assigned to a node n, and γ is a probability (nodeaccommodation probability) that the total of capacities of linksterminating at a node n and capacities of paths i_(p) terminating at thenode n can be accommodated in the node n.
 5. The method according toclaim 4, wherein the step d) comprises the steps of: d-1) converting thestochastic path accommodation constraint to a determinate pathaccommodation constraint on condition that the requested capacity of thedemand follows a normal distribution having a mean μ_(p) and a varianceσ_(p), wherein the determinate path accommodation constraint isrepresented by:${\sum\limits_{i_{p} = 1}^{Ip}\quad c_{ip}} \geq {\mu_{p} + {{t(\alpha)}\sigma_{p}\quad \left( {{p = 1},\cdots \quad,P} \right)}}$

 where t(α) is a safety coefficient of a standard normal distributionsatisfying α; and d-2) converting the stochastic node accommodationconstraint to a determinate node accommodation constraint on conditionthat a sum of o_(p/n)v_(p) for p=1, . . . , P follows a normaldistribution having a mean μ_(n) and a variance σ_(n), wherein the meanμ_(n) and the variance σ_(n) are represented by:${\mu_{n} = {{\sum\limits_{p - 1}^{P}{\quad o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)\quad {{and}\left( \sigma_{n} \right)}^{2}}} = {\sum\limits_{p - 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}}},{respectively},$

 and the determinate node accommodation constraint is represented by:${{{v\quad e_{n}} - {\sum\limits_{l - 1}^{L}\quad {h_{l/n}d}}} \geq {\mu_{n} + {t(\gamma)\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}},$

 (n=1, . . . , N), where t(γ) is a safety coefficient of a standardnormal distribution satisfying γ.
 6. The method according to claim 5,wherein the equivalent determinate programming problem consists of: theobjective function represented by:${\sum\limits_{l = 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n = 1}^{N}\quad e_{n}}}$

 where ω_(l) is a cost coefficient of a link l and ε is a costcoefficient of a node, and the determinate constraints consisting of:the determinate path accommodation constraint represented by:${{\sum\limits_{i_{p} - 1}^{Ip}\quad c_{ip}} \geq {\mu_{p} + {{t(\alpha)}\sigma_{p}\quad \left( {{p = 1},\cdots \quad,P} \right)}}},$

the link accommodation constraint represented by:${{\sum\limits_{p = 1}^{P}\quad {\sum\limits_{i_{p} - 1}^{Ip}\quad {g_{{ip}/1}c_{lp}}}} \leq {\lambda \quad d_{1}\quad \left( {{1 = 1},\cdots \quad,L} \right)}},{and}$

the determinate node accommodation constraint represented by:${{v\quad e_{n}} - {\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad {\left( {{n = 1},\ldots \quad,N} \right).}}}$


7. The method according to claim 1, wherein the step c) comprises thesteps of: c-1) generating a path accommodation constraint for causingthe requested capacity of the demand to be accommodated in the pathcandidates; c-2) generating a stochastic link accommodation constraintfor causing capacities assigned to path candidates to be accommodated inthe links; and c-3) generating a stochastic node accommodationconstraint for causing a total of capacities of path candidates passingthrough a node to be accommodated in the node.
 8. The method accordingto claim 7, wherein, in the step c-1), the path accommodation constraintcauses a total of ratios of capacities assigned to path candidates of ademand to be at least 1 when it is assumed that the requested capacityof the demand is 1, in the step c-2), the stochastic link accommodationconstraint causes a probability that a capacity of a link exceeds thetotal of capacities of path candidates passing through the link to be atleast a predetermined link accommodation probability, and in the stepc-3), the stochastic node accommodation constraint causes a probabilitythat a node capacity exceeds a total of termination capacity of a linkand termination capacity of the demand to be at least a predeterminednode accommodation probability.
 9. The method according to claim 8,wherein the path accommodation constraint generated in the step c-1) isrepresented by:${\sum\limits_{{ip} = 1}^{Ip}\quad r_{ip}} \geqq {1\quad \left( {{p = 1},\ldots \quad,P} \right)}$

where p is a demand number, i_(p) is a candidate, number of a demand pin the range of 1, . . . , I_(p), where a path candidate i_(p) of ademand p is an arbitrary path between an originating node and aterminating node of a demand p, and r_(ip) is a ratio (real numbervariable) assigned to a path candidate i_(p) when it is assumed that arequested capacity of a demand p is l, the stochastic link accommodationconstraint generated by the step c-2) is represented by:${{Prob}\left\lbrack {{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}v_{p}r_{ip}}}} \leq {\lambda \quad d_{1}}} \right\rbrack} \geq \beta$

 (l=1, . . . , L) where Prob [ ] represents a probability that thecondition in [ ] is satisfied. l: a link number, g_(ip/l) is anindicator indicating l when a path candidate i_(p) of a demand p passesthrough a link l (as represented by ip/l) and indicating 0 otherwise, d₁is a capacity (integer variable) assigned to a link l, λ is a capacityof a link, v_(p) is a requested capacity (random variable) of a demandp, and β: a probability (link accommodation probability) that the totalof capacities of paths i_(p) passing through a link l can beaccommodated in the link l, and the stochastic node accommodationconstraint generated by the step c-3) is represented by:${{Prob}\left\lbrack {{{\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p - 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {v\quad e_{n}}} \right\rbrack} \geq \gamma$

 (n=1, . . . , N) where n is a node number, h_(l/n) is an indicatorindicating l when a link l passes though node n (as represented by l/n)and indicating 0 otherwise, o_(p/n) is an indicator indicating l when ademand p terminates at a node n (as represented by p/n) and indicating 0otherwise, ν is a capacity of a node, e_(n) is a capacity (integervariable) assigned to a node n, and γ is a probability (nodeaccommodation probability) that the total of capacities of linksterminating at a node n and capacities of paths i_(p) terminating at thenode n can be accommodated in the node n.
 10. The method according toclaim 9, wherein the step d) comprises the steps of: d-1) converting thestochastic link accommodation constraint to a determinate linkaccommodation constraint on condition that the requested capacity of thedemand follows a normal distribution having a mean μ_(p) and a varianceσ_(p), and a sum of g_(ip/l)v_(p)r_(ip) for p=1, . . . , P, i=1, . . . ,i_(p) is follows probability distribution having a mean μ_(l) and avariance a σ_(l) that are represented by:${\mu_{1} = {{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}r_{lp}\mu_{p}\quad \left( {{l = 1},\ldots \quad,L} \right)\quad {{and}\left( \sigma_{1} \right)}^{2}}}} = {\sum\limits_{p = 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {{g_{{ip}/1}\left( r_{ip} \right)}^{2}\left( \sigma_{p} \right)^{2}\quad \left( {{l = 1},\ldots \quad,L} \right)}}}}},$

respectively, and further on condition that a sum of g_(ip/l)v_(p)r_(ip)for p=1, . . . , P, i_(p)=1, . . . , I_(p) follows a normaldistribution, wherein the determinate link accommodation constraint isrepresented by: λd _(l)≧μ_(l) +t(β)σ_(l) (l=1, . . . , L)  where t(β) isa safety coefficient of a standard normal distribution satisfying β, andd-2) converting the stochastic node accommodation constraint to adeterminate node accommodation constraint on condition that a sum ofo_(p/n)v_(p) for p=1, . . . , P follows a normal distribution having amean μ_(n) and a variance σ_(n), wherein the mean μ_(n) and the varianceare represented by:${\mu_{n} = {{\sum\limits_{p - 1}^{P}\quad {o_{p/n}\mu_{p}\quad \left( {{n = 1},\ldots \quad,N} \right)\quad {{and}\left( \sigma_{n} \right)}^{2}}} = {\sum\limits_{p - 1}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\ldots \quad,N} \right)}}}},{respectively},$

 and the determinate node accommodation constraint is represented by:${{ve}_{n} - {\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}}}$

 (n=1, . . . , N) where t(γ) is a safety coefficient of a standardnormal distribution satisfying γ.
 11. The method according to claim 10,wherein the equivalent determinate programming problem consists of: theobjective function represented by:${\sum\limits_{l = 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n = 1}^{N}\quad e_{n}}}$

where ω_(l) is a cost coefficient of a link l and ε is a costcoefficient of a node, and the determinate constraints consisting of:the path accommodation constraint represented by:${{\sum\limits_{{ip} - 1}^{Ip}\quad r_{ip}} \geqq {1\quad \left( {{p = 1},\ldots \quad,P} \right)}},$

the determinate link accommodation constraint represented by: λd_(l)≧μ_(l) +t(β)σ_(l) (l=1, . . . , L), and the determinate nodeaccommodation constraint represented by:${{ve}_{n} - {\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad {\left( {{n = 1},\ldots \quad,N} \right).}}}$


12. The method according to claim 7, wherein, in the step c-1), the pathaccommodation constraint causes a total of capacities assigned to pathcandidates of a demand to be at least the requested capacity of thedemand, in the step c-2), the stochastic link accommodation constraintcauses a probability that a capacity of a link exceeds a total ofcapacities of paths passing through the link to be at least apredetermined link accommodation probability, and in the step c-3), thestochastic node accommodation constraint causes a probability that anode capacity exceeds a total of termination capacity of a link andtermination capacity of the demand to be at least a predetermined nodeaccommodation probability.
 13. The method according to claim 12, whereinthe path accommodation constraint generated in the step c-1) isrepresented by:${{\sum\limits_{{ip} - 1}^{Ip}\quad c_{lp}} \geqq {v_{p}\quad \left( {{p = 1},\cdots \quad,P} \right)}},$

where p is a demand number, i_(p) is a candidate number of a demand p inthe range of 1, . . . , I_(p), where a path candidate i_(p) of a demandp is an arbitrary path between an originating node and a terminatingnode of a demand p, c_(ip) is a capacity as a random variable assignedto a path candidate i_(p), and v_(p) is a requested capacity (randomvariable) of a demand p, the stochastic link accommodation constraintgenerated by the step c-2) is represented by:${{Prob}\left\lbrack {{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} = 1}^{Ip}\quad {g_{{ip}/1}v_{p}r_{ip}}}} \leq {\lambda \quad d_{1}}} \right\rbrack} \geq {\beta \quad \left( {{l = 1},\cdots \quad,L} \right)}$

where Prob [ ] represents a probability that the condition in [ ] issatisfied, l: a link number, g_(ip/l) is an indicator indicating l whena path candidate i_(p) of a demand p passes through a link l (asrepresented by ip/l) and indicating 0 otherwise, d_(l) is a capacity(integer variable) assigned to a link λ is a capacity of a link, v_(p)is a requested capacity (random variable) of a demand p, and r_(ip) is aratio (real number variable) assigned to a path candidate i_(p) when itis assumed that a requested capacity of a demand p is l, β: aprobability (link accommodation probability) that the total ofcapacities of paths i_(p) passing through a link l can be accommodatedin the link l, and the stochastic node accommodation constraintgenerated by the step c-3) is represented by:${{Prob}\left\lbrack {{{\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p = 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {\nu \quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}$

where n is a node number, h_(l/n) is an indicator indicating l when alink l passes though node n (as represented by l/n) and indicating 0otherwise, o_(p/n) is an indicator indicating l when a demand pterminates at a node n (as represented by p/n) and indicating 0otherwise, ν is a capacity of a node, e_(n) is a capacity (integervariable) assigned to a node n, and γ is a probability (nodeaccommodation probability) that the total of capacities of linksterminating at a node n and capacities of paths i_(p) terminating at thenode n can be accommodated in the node n.
 14. The method according toclaim 13, wherein the step d) comprises the steps of: d-1) convertingthe stochastic link accommodation constraint to a determinate linkaccommodation constraint on condition that the requested capacity of thedemand follows a normal distribution having a mean μ_(p) and a varianceσ_(p), wherein a mean μ_(ip) and a variance σ_(ip) of a random variablec_(ip) is represented by:${\sum\limits_{{ip} - 1}^{Ip}\quad \mu_{ip}} = {\mu_{p}\quad \left( {{p = 1},\cdots \quad,P} \right)\quad {and}}$${{\sum\limits_{{ip} - 1}^{Ip}\quad \left( \sigma_{ip} \right)^{2}} = {\left( \sigma_{p} \right)^{2}\quad \left( {{p = 1},\cdots \quad,P} \right)}},{respectively},{and}$

 a sum of g_(ip/l)v_(p)r_(ip) for p=1, . . . , P and i_(p)=1, . . . ,I_(p) follows a probability distribution having a mean μ_(l) and avariance σ_(l) that are represented by:${\mu_{1} = {{\sum\limits_{p - 1}^{P}{\quad {\sum\limits_{{ip} = 1}^{Ip}{\quad g_{{ip}/1}\mu_{lp}\quad \left( {{l = 1},\cdots \quad,L} \right)\quad {{and}\left( \sigma_{1} \right)}^{2}}}}} = {\sum\limits_{p - 1}\quad {\sum\limits_{{ip} = 1}^{Ip}\quad {{g_{{ip}/1}\left( \sigma_{ip} \right)}^{2}\quad \left( {{l = 1},\cdots \quad,L} \right)}}}}},{respectively},$

 and further on condition that a sum of g_(ip/l)v_(p)r_(ip) for p=1, . .. , P and i_(p=)1, . . . , I_(p) follows a normal distribution, whereinthe determinate link accommodation constraint is represented by: λd_(l)≧μ_(l) +t(β)σ_(l) (l=1, . . . , L) where t(β) is a safetycoefficient of a standard normal distribution satisfying β, and d-2)converting the stochastic node accommodation constraint to a determinatenode accommodation constraint on condition that a sum of o_(p/n)v_(p)for p=1, . . . , P follows a normal distribution having a mean μ_(n) anda variance σ_(n), wherein the mean μ_(n) and the variance σ_(n) arerepresented by:${\mu_{n} = {{\sum\limits_{p - 1}^{P}{\quad o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)\quad {{and}\left( \sigma_{n} \right)}^{2}}} = {\sum\limits_{p - 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}}},{respectively},$

 and the determinate node accommodation constraint is represented by:${{{\nu \quad e_{n}} - {\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {t(\gamma)\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}},$

where t(γ) is a safety coefficient of a standard normal distributionsatisfying γ.
 15. The method according to claim 14, wherein theequivalent determinate programming problem consists of: the objectivefunction represented by:${\sum\limits_{l - 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}$

where ω_(l) is a cost coefficient of a link l and ε is a costcoefficient of a node, and the determinate constraints consisting of:the path accommodation constraint represented by:${{\sum\limits_{{ip} = 1}^{Ip}\quad c_{ip}} \geqq {v_{p}\quad \left( {{p = 1},\cdots \quad,P} \right)}},$

the determinate link accommodation constraint represented by:  λd_(l)≧μ_(l) +t(β)σ_(l) (l=1, . . . , L) and the determinate nodeaccommodation constraint represented by:${{\nu \quad e_{n}} - {\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad {\left( {{n = 1},\cdots \quad,N} \right).}}}$


16. The method according to claim 2, wherein, in the step c-1), thestochastic path accommodation constraint causes a probability that atotal of capacities assigned to path candidates of a demand in a networkstate is not smaller than the requested capacity of the demand to be atleast a predetermined path accommodation probability, wherein thenetwork state indicates one of a normal state and fault states for somelink, in the step c-2), the link accommodation constraint causes a totalof capacities of path candidates passing through a link in the networkstate to be accommodated in the link, and in the step c-3), thestochastic node accommodation constraint causes a probability that acapacity assigned to a node exceeds a total of termination capacity of alink and termination capacity of the demand to be at least apredetermined node accommodation probability.
 17. The method accordingto claim 16, wherein the stochastic path accommodation constraintgenerated in the step c-1) is represented by:${{{Prob}\left\lbrack {{\sum\limits_{i_{p} - 1}^{Ip}\quad c_{{ip}\quad ɛ}} \geq v_{p}} \right\rbrack} \geq {\alpha \quad \left( {{p = 1},\cdots \quad,P,\quad {{{and}\quad s} = 0},\cdots \quad,S} \right)}},$

where Prob [ ] represents a probability that the condition in [ ] issatisfied, p is a demand number, i_(p) is a candidate number of a demandp in the range of 1, . . . , I_(p), where a path candidate i_(p) of ademand p is an arbitrary path between an originating node and aterminating node of a demand p, s is a network state in the range of 0,. . . , S, where 0 represents a normal state where no fault occurs, andeach of 1, . . . , S represents a fault state in which there is a faulton some link, c_(ipε): a capacity (integer variable) assigned to a pathi_(p) of a demand p in a state s, v_(p) is a requested capacity (randomvariable) of a demand p, and α is a probability (path accommodationprobability) that the requested capacity v_(p) of a demand p is assignedto path candidates of the demand p: the link accommodation constraintgenerated by the step c-2) is represented by:${\sum\limits_{p - 1}^{P}\quad {\sum\limits_{i_{p} - 1}^{Ip}\quad {g_{{ip}/1}c_{{ip}\quad ɛ}}}} \leq {\lambda \quad d_{1}\quad \left( {{l = 1},\cdots \quad,L,\quad {{{and}\quad s} = 0},\cdots \quad,S} \right)}$

 (l=1, . . . , L, and s=0, . . . , S) where l: a link number, g_(ip/l)is an indicator indicating l when a path candidate i_(p) of a demand ppasses through a link l (as represented by ip/l) and indicating 0otherwise, d_(l) is a capacity (integer variable) assigned to a link l,and λ is a capacity of a link, and the stochastic node accommodationconstraint generated by the step c-3) is represented by:${{Prob}\left\lbrack {{{\sum\limits_{l = 1}^{L}\quad {h_{l/1}d_{1}}} + {\sum\limits_{p = 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {\nu \quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}$

where n is a node number, h_(l/n) is an indicator indicating l when alink l passes though node n (as represented by l/n) and indicating 0otherwise, o_(p/n) is an indicator indicating l when a demand pterminates at a node n (as represented by p/n) and indicating 0otherwise, 84 is a capacity of a node, e_(n) is a capacity (integervariable) assigned to a node n, and γ is a probability (nodeaccommodation probability) that the total of capacities of linksterminating at a node n and capacities of paths i_(p) terminating at thenode n can be accommodated in the node n.
 18. The method according toclaim 17, wherein the step d) comprises the steps of: d-1) convertingthe stochastic path accommodation constraint to a determinate pathaccommodation constraint on condition that the requested capacity of thedemand follows a normal distribution having a mean μ_(p) and a varianceσ_(p), wherein the determinate path accommodation constraint isrepresented by:${\sum\limits_{i_{p} = 1}^{Ip}\quad c_{{ip}\quad ɛ}} \geq {\mu_{p} + {{t(\alpha)}\sigma_{p}\quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}}$

 where t(α) is a safety coefficient of a standard normal distributionsatisfying α; and d-2) converting the stochastic node accommodationconstraint to a determinate node accommodation constraint on conditionthat a sum of o_(p/n)v_(p) for p=1, . . . , P follows a normaldistribution having a mean μ_(n) and a variance σ_(n), wherein the meanμ_(n) and the variance σ_(n) are represented by:${\mu_{n} = {{\sum\limits_{p - 1}^{P}{\quad o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)\quad {{and}\left( \sigma_{n} \right)}^{2}}} = {\sum\limits_{p = 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}}},{respectively},$

and the determinate node accommodation constraint is represented by:${{{\nu \quad e_{n}} - {\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {t(\gamma)\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}},$

 (n=1, . . . , N), where t(γ) is a safety coefficient of a standardnormal distribution satisfying γ.
 19. The method according to claim 18,wherein the equivalent determinate programming problem consists of: theobjective function represented by:${\sum\limits_{l - 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}$

where ω_(l) is a cost coefficient of a link l and ε is a costcoefficient of a node, and the determinate constraints consisting of:the determinate path accommodation constraint represented by:${{\sum\limits_{i_{p} = 1}^{Ip}\quad c_{ipe}} \geq {\mu_{p} + {{t(\alpha)}\sigma_{p}\quad \left( {{p = 1},\cdots \quad,P,{s = 0},\cdots \quad,S} \right)}}},$

the link accommodation constraint represented by:${{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{i_{p} = 1}^{Ip}\quad {g_{{ip}/1}c_{ip}}}} \leq {\lambda \quad d_{1}\quad \left( {{l = 1},\cdots \quad,L,\quad {{{and}\quad s} = 0},\cdots \quad,S} \right)}},\quad {and}$

the determinate node accommodation constraint represented by:${\nu \quad e_{n}} = {{\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad {\left( {{n = 1},\cdots \quad,N} \right).}}}}$


20. The method according to claim 7, wherein, in the step c-1), the pathaccommodation constraint causes a total of ratios of capacities assignedto path candidates of a demand to be at least l when it is assumed thatthe requested capacity of the demand is 1, in the step c-2), thestochastic link accommodation constraint causes a probability that acapacity of a link exceeds the total of capacities of path candidatespassing through the link in a network state to be at least apredetermined link accommodation probability, wherein the network stateindicates one of a normal state and fault states for some link, and inthe step c-3), the stochastic node accommodation constraint causes aprobability that a node capacity exceeds a total of termination capacityof a link and termination capacity of the demand to be at least apredetermined node accommodation probability.
 21. The method accordingto claim 20, wherein the path accommodation constraint generated in thestep c-1) is represented by:${\sum\limits_{{ip} = 1}^{Ip}\quad r_{{ip}\quad ɛ}} \geqq {1\quad \left( {{p = 1},\cdots \quad,P} \right)}$

where p is a demand number, i_(p) is a candidate number of a demand p inthe range of 1, . . . , I_(p), where a path candidate i_(p) of a demandp is an arbitrary path between an originating node and a terminatingnode of a demand p, r_(ips) is a ratio (real number variable) assignedto a path candidate i_(p) when it is assumed that the requested capacityof a demand p is l in a state s, and s is a network state in the rangeof 0, . . . , S, where 0 represents a normal state where no faultoccurs, and each of 1, . . . , S represents a fault state in which thereis a fault on some link, the stochastic link accommodation constraintgenerated by the step c-2) is represented by:${{Prob}\left\lbrack {{\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} = 1}^{Ip}\quad {g_{{ip}/1}v_{p}r_{{ip}\quad ɛ}}}} \leq {f_{l/s}\lambda \quad d_{1}}} \right\rbrack} \geq \beta$

 (l=1, . . . , L, and s=0, . . . , S)  where Prob [ ] represents aprobability that the condition in [ ] is satisfied, l is a link number,g_(ip/l) is an indicator indicating l when a path candidate i_(p) of ademand p passes through a link l (as represented by ip/l) and indicating0 otherwise, d_(l) is a capacity (integer variable) assigned to a linkl, f_(l/ε) is an indicator indicating 0 when a link l is faulty, andindicating l when the link l is normal, wherein in the normal staterepresented as s=0, f_(l/ε)=1 in every link l. λ is a capacity of alink, v_(p) is a requested capacity (random variable) of a demand p, andβ: a probability (link accommodation probability) that the total ofcapacities of paths i_(p) passing through a link l can be accommodatedin the link l, and the stochastic node accommodation constraintgenerated by the step c-3) is represented by:${{Prob}\left\lbrack {{{\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p - 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {\nu \quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}$

 (n=1, . . . , N) where n is a node number, h_(l/n) is an indicatorindicating l when a link l passes though node n (as represented by l/n)and indicating 0 otherwise, o_(p/n) is an indicator indicating l when ademand p terminates at a node n (as represented by p/n) and indicating 0otherwise, ν is a capacity of a node, e_(n) is a capacity (integervariable) assigned to a node n, and γ is a probability (nodeaccommodation probability) that the total of capacities of linksterminating at a node n and capacities of paths i_(p) terminating at thenode n can be accommodated in the node n.
 22. The method according toclaim 21, wherein the step d) comprises the steps of: d-1) convertingthe stochastic link accommodation constraint to a determinate linkaccommodation constraint on condition that the requested capacity of thedemand follows a normal distribution having a mean μ_(p) and a varianceσ_(p), and a sum of g_(ip/l)v_(p)r_(ips) for p=1, . . . , P, i=1, . . ., i_(p) follows probability distribution having a mean μ_(l) and avariance σ_(l) that are represented by:${\mu_{1} = {{\sum\limits_{p - 1}^{P}{\quad {\sum\limits_{{ip} - 1}^{Ip}{\quad g_{{ip}/1}r_{{ip}\quad ɛ}\mu_{p}\quad \left( {{l = 1},\cdots \quad,L} \right)\quad {{and}\left( \sigma_{1} \right)}^{2}}}}} = {\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {{g_{{ip}/1}\left( r_{{ip}\quad ɛ} \right)}^{2}\left( \sigma_{p} \right)^{2}\quad \left( {{l = 1},\cdots \quad,L} \right)}}}}},$

respectively, and further on condition that a sum ofg_(ip/l)v_(p)r_(ips) for p=1, . . . , P, i_(p)=1, . . . , I_(p) followsa normal distribution, wherein the determinate link accommodationconstraint is represented by: λd _(l)≧μ_(l) +t(β)σ_(l) (l=1, . . . , L) where t(β) is a safety coefficient of a standard normal distributionsatisfying β, and d-2) converting the stochastic node accommodationconstraint to a determinate node accommodation constraint on conditionthat a sum of o_(p/n)v_(p) for p=1, . . . , P follows a normaldistribution having a mean μ_(n) and a variance σ_(n), wherein the meanμ_(n) and the variance σ_(n) are represented by:${\mu_{n} = {{\sum\limits_{p - 1}^{P}{\quad o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)\quad {{and}\left( \sigma_{n} \right)}^{2}}} = {\overset{P}{\sum\limits_{p - 1}}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}}},{respectively},$

 and the determinate node accommodation constraint is represented by:${{{\nu \quad e_{n}} - {\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {t(\gamma)\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}},$

where t(γ) is a safety coefficient of a standard normal distributionsatisfying γ.
 23. The method according to claim 22, wherein theequivalent determinate programming problem consists of: the objectivefunction represented by:${\sum\limits_{l - 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}$

where ω_(l) is a cost coefficient of a link l and ε is a costcoefficient of a node, and the determinate constraints consisting of:the path accommodation constraint represented by:${{\sum\limits_{{ip} = 1}^{Ip}\quad r_{ips}} \geqq {1\quad \left( {{p = 1},\cdots \quad,P,{{{and}\quad s} = 0},\cdots \quad,S} \right)}},$

the determinate link accommodation constraint represented by:  λd_(l)≧μ_(l) +t(β)σ_(l) (l=1, . . . , L), and the determinate nodeaccommodation constraint represented by:${{\nu \quad e_{n}} - {\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad {\left( {{n = 1},\cdots \quad,N} \right).}}}$


24. The method according to claim 7, wherein, in the step c-1), the pathaccommodation constraint causes a total of capacities assigned to pathcandidates of a demand in a network state to be at least the requestedcapacity of the demand, wherein indicates one of a normal state andfault states for some link, in the step c-2), the stochastic linkaccommodation constraint causes a probability that a capacity of a linkexceeds a total of capacities of paths passing through the link in thenetwork state to be at least a predetermined link accommodationprobability, and in the step c-3), the stochastic node accommodationconstraint causes a probability that a node capacity exceeds a total oftermination capacity of a link and termination capacity of the demand tobe at least a predetermined node accommodation probability.
 25. Themethod according to claim 24, wherein the path accommodation constraintgenerated in the step c-1) is represented by:${\sum\limits_{{ip} = 1}^{Ip}\quad c_{{ip}\quad ɛ}} \geqq {v_{p}\quad {\left( {{p = 1},\cdots \quad,P} \right).}}$

where p is a demand number, i_(p) is a candidate number of a demand p inthe range of 1, . . . , I_(p), where a path candidate i_(p) of a demandp is an arbitrary path between an originating node and a terminatingnode of a demand p, s is a network state in the range of 0, . . . , S,where 0 represents a normal state where no fault occurs, and each of 1,. . . , S represents a fault state in which there is a fault on somelink, c_(ips): a capacity (integer variable) assigned to a path i_(p) ofa demand p in a state s, and v_(p) is a requested capacity (randomvariable) of a demand the stochastic link accommodation constraintgenerated by the step c-2) is represented by:${{Prob}\left\lbrack {{\sum\limits_{p = 1}^{P}\quad {\sum\limits_{{ip} - 1}^{Ip}\quad {g_{{ip}/1}c_{{ip}\quad ɛ}}}} \leq {f_{1/s}\lambda \quad d_{1}}} \right\rbrack} \geq {\beta \quad \left( {{l = 1},\cdots \quad,L,{{{and}\quad s} = 0},\cdots \quad,S} \right)}$

 (l=1, . . . , L, and s=0, . . . , S) where Prob [ ] represents aprobability that the condition in [ ] is satisfied, l: a link number,g_(ip/l) is an indicator indicating 1 when a path candidate i_(p) of ademand p passes through a link l (as represented by ip/l) and indicating0 otherwise, d_(l) is a capacity (integer variable) assigned to a linkl, f_(l/s) is an indicator indicating 0 when a link l is faulty, andindicating l when the link l is normal, wherein in the normal staterepresented as s=0, f_(l/s)=1 in every link l, λ is a capacity of alink, β: a probability (link accommodation probability) that the totalof capacities of paths i_(p) passing through a link l can beaccommodated in the link l, and the stochastic node accommodationconstraint a generated by the step c-3) is represented by:${{Prob}\left\lbrack {{{\sum\limits_{l - 1}^{L}\quad {h_{l/n}d_{1}}} + {\sum\limits_{p - 1}^{P}\quad {o_{p/n}{v_{p}/\lambda}}}} \leq {\nu \quad e_{n}}} \right\rbrack} \geq {\gamma \quad \left( {{n = 1},\cdots \quad,N} \right)}$

where n is a node number, h_(l/n) is an indicator indicating l when alink l passes though node n (as represented by l/n) and indicating 0otherwise, o_(p/n) is an indicator indicating l when a demand pterminates at a node n (as represented by p/n) and indicating 0otherwise, ν is a capacity of a node, e_(n) is a capacity (integervariable) assigned to a node n, and γ is a probability (nodeaccommodation probability) that the total of capacities of linksterminating at a node n and capacities of paths i_(p) terminating at thenode n can be accommodated in the node n.
 26. The method according toclaim 25, wherein the step d) comprises the steps of: d-1) convertingthe stochastic link accommodation constraint to a determinate linkaccommodation constraint on condition that the requested capacity of thedemand follows a normal distribution having a mean μ_(p) and a varianceσ_(p), wherein a mean μ_(ipa) and a variance a σ_(ipε) of a randomvariable c_(ips) is represented by:${\sum\limits_{{ip} = 1}^{Ip}\quad \mu_{{ip}\quad ɛ}} = {\mu_{p}\quad \left( {{p = 1},\cdots \quad,{{P\quad {and}\quad s} = 0},\cdots \quad,S} \right)}$and${{\sum\limits_{{ip} - 1}^{Ip}\quad \left( \sigma_{{ip}\quad ɛ} \right)^{2}} = {\left( \sigma_{p} \right)^{2}\quad \left( {{p = 1},\cdots \quad,{{P\quad {and}\quad s} = 0},\cdots \quad,S} \right)}},$

respectively, and a sum of g_(ip/l)c_(ips) for p=1, . . . , P andi_(p)=1, . . . , I_(p) follows a probability distribution having a meanμ_(ls) and a variance σ_(lε) that are represented by:$\mu_{1c} = {\sum\limits_{p = 1}^{P}{\quad {\sum\limits_{{ip} - 1}^{Ip}{\quad g_{{ip}/1}\mu_{{ip}\quad ɛ}\quad \left( {{l = 1},\cdots \quad,{{L\quad {and}\quad s} = 0},\cdots \quad,S} \right)}}}}$${{and}\left( \sigma_{1} \right)}^{2} = {\sum\limits_{p - 1}^{P}\quad {\sum\limits_{{ip} = 1}^{Ip}\quad \left( {g_{{ip}/1}\left( \sigma_{{ip}\quad ɛ} \right)} \right)^{2}}}$

(l=1, . . . , L and s=0, . . . , S), respectively, and further oncondition that a sum of g_(ip/l)c_(ips) for p=1, . . . , P and i_(p)=1,. . . , I_(p) follows a normal distribution, wherein the determinatelink accommodation constraint is represented by: λf _(lε)≧μ_(ls)+t(β)σ_(ls) (l=1, . . . , L and s=0, . . . , S)  where t(β) is a safetycoefficient of a standard normal distribution satisfying β, and d-2)converting the stochastic node accommodation constraint to a determinatenode accommodation constraint on condition that a sum of o_(p/n)v_(p)for p=1, . . . , P follows a normal distribution having a mean μ_(n) anda variance σ_(n), wherein the mean μ_(n) and the variance σ_(n) arerepresented by:${\mu_{n} = {{\sum\limits_{p - 1}^{P}{\quad o_{p/n}\mu_{p}\quad \left( {{n = 1},\cdots \quad,N} \right)\quad {{and}\left( \sigma_{1} \right)}^{2}}} = {\sum\limits_{p = 1}^{P}\quad {{o_{p/n}\left( \sigma_{p} \right)}^{2}\quad \left( {{n = 1},\cdots \quad,N} \right)}}}},{respectively},$

 and the determinate node accommodation constraint is represented by:${{{\nu \quad e_{n}} - {\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {t(\gamma)\sigma_{n}\quad \left( {{n = 1},\cdots \quad,N} \right)}}},$

 (n=1, . . . , N) where t(γ) is a safety coefficient of a standardnormal distribution satisfying γ.
 27. The method according to claim 26,wherein the equivalent determinate programming problem consists of: theobjective function represented by:${\sum\limits_{l - 1}^{L}\quad {\omega_{1}d_{1}}} + {ɛ{\sum\limits_{n - 1}^{N}\quad e_{n}}}$

where ω_(l) is a cost coefficient of a link l and ε is a costcoefficient of a node, and the determinate constraints consisting of:the path accommodation constraint represented by:${{\sum\limits_{{ip} = 1}^{Ip}\quad c_{ips}} \geqq {v_{p}\quad \left( {{p = 1},\cdots \quad,{{P\quad {and}\quad s} = 0},\cdots \quad,S} \right)}},$

the determinate link accommodation constraint represented by: λf_(lε)≧μ_(ls) +t(β)σ_(ls) (l=1, . . . , L and s=0, . . . , S) and thedeterminate node accommodation constraint represented by:${{\nu \quad e_{n}} - {\sum\limits_{l = 1}^{L}\quad {h_{l/n}d_{1}}}} \geq {\mu_{n} + {{t(\gamma)}\sigma_{n}\quad {\left( {{n = 1},\cdots \quad,N} \right).}}}$


28. A system for designing a communication network composed of aplurality of nodes and links each connecting two nodes, comprising: aninput means for inputting network data including a requested capacity ofa demand as a random variable following a predetermined probabilitydistribution between any two nodes and path candidates of the demand foraccommodating the requested capacity of the demand; a first generatorfor generating an objective function representing a total cost of thenodes and the links from the network data; a second generator forgenerating a predetermined set of stochastic constraints by using therequested capacity of the demand to produce a stochastic programmingproblem including the objective function and the stochastic constraints;a converter for converting the stochastic programming problem into anequivalent determinate programming problem on condition of thepredetermined probability distribution; and an optimizing means forsolving the determinate programming problem to determine capacities ofthe nodes and the links so that the objective function is minimized. 29.The system according to claim 28, wherein the second generator generatesa stochastic path accommodation constraint for causing the requestedcapacity of the demand to be accommodated in the path candidates,generates a link accommodation constraint for causing capacitiesassigned to path candidates to be accommodated in the links, andgenerates a stochastic node accommodation constraint for causing a totalof capacities of path candidates passing through a node to beaccommodated in the node.
 30. The system according to claim 29, whereinthe stochastic path accommodation constraint causes a probability that atotal of capacities assigned to path candidates of a demand is notsmaller than the requested capacity of the demand to be at least apredetermined path accommodation probability, the link accommodationconstraint causes a total of capacities of path candidates passingthrough a link to be accommodated in the link, and the stochastic nodeaccommodation constraint causes a probability that a capacity assignedto a node exceeds a total of termination capacity of a link andtermination capacity of the demand to be at least a predetermined nodeaccommodation probability.
 31. The system according to claim 28, whereinthe second generator generates a path accommodation constraint forcausing the requested capacity of the demand to be accommodated in thepath candidates, generates a stochastic link accommodation constraintfor causing capacities assigned to path candidates to be accommodated inthe links, and generates a stochastic node accommodation constraint forcausing a total of capacities of path candidates passing through a nodeto be accommodated in the node.
 32. The system according to claim 31,wherein, the path accommodation constraint causes a total of ratios ofcapacities assigned to path candidates of a demand to be at least 1 whenit is assumed that the requested capacity of the demand is 1, thestochastic link accommodation constraint causes a probability that acapacity of a link exceeds the total of capacities of path candidatespassing through the link to be at least a predetermined linkaccommodation probability, and the stochastic node accommodationconstraint causes a probability that a node capacity exceeds a total oftermination capacity of a link and termination capacity of the demand tobe at least a predetermined node accommodation probability.
 33. Thesystem according to claim 31, wherein, the path accommodation constraintcauses a total of capacities assigned to path candidates of a demand tobe at least the requested capacity of the demand, the stochastic linkaccommodation constraint causes a probability that a capacity of a linkexceeds a total of capacities of paths passing through the link to be atleast a predetermined link accommodation probability, and the stochasticnode accommodation constraint causes a probability that a node capacityexceeds a total of termination capacity of a link and terminationcapacity of the demand to be at least a predetermined node accommodationprobability.
 34. The system according to claim 29, wherein, thestochastic path accommodation constraint causes a probability that atotal of capacities assigned to path candidates of a demand in a networkstate is not smaller than the requested capacity of the demand to be atleast a predetermined path accommodation probability, wherein thenetwork state indicates one of a normal state and fault states for somelink, the link accommodation constraint causes a total of capacities ofpath candidates passing through a link in the network state to beaccommodated in the link, and the stochastic node accommodationconstraint causes a probability that a capacity assigned to a nodeexceeds a total of termination capacity of a link and terminationcapacity of the demand to be at least a predetermined node accommodationprobability.
 35. The system according to claim 31, wherein, the pathaccommodation constraint causes a total of ratios of capacities assignedto path candidates of a demand to be at least 1 when it is assumed thatthe requested capacity of the demand is 1, the stochastic linkaccommodation constraint causes a probability that a capacity of a linkexceeds the total of capacities of path candidates passing through thelink in a network state to be at least a predetermined linkaccommodation probability, wherein the network state indicates one of anormal state and fault states for some link, and the stochastic nodeaccommodation constraint causes a probability that a node capacityexceeds a total of termination capacity of a link and terminationcapacity of the demand to be at least a predetermined node accommodationprobability.
 36. The system according to claim 31, wherein, the pathaccommodation constraint causes a total of capacities assigned to pathcandidates of a demand in a network state to be at least the requestedcapacity of the demand, wherein indicates one of a normal state andfault states for some link, the stochastic link accommodation constraintcauses a probability that a capacity of a link exceeds a total ofcapacities of paths passing through the link in the network state to beat least a predetermined link accommodation probability, and thestochastic node accommodation constraint causes a probability that anode capacity exceeds a total of termination capacity of a link andtermination capacity of the demand to be at least a predetermined nodeaccommodation probability.
 37. A recording medium storing a networkdesigning control program which causes a computer to designing acommunication network composed of a plurality of nodes and links eachconnecting two nodes, the network designing control program comprisingthe steps of: a) inputting network data including a requested capacityof a demand as a random variable following a predetermined probabilitydistribution between any two nodes and path candidates of the demand foraccommodating the requested capacity of the demand; b) generating anobjective function representing a total cost of the nodes and the linksfrom the network data; c) generating a predetermined set of stochasticconstraints by using the requested capacity of the demand to produce astochastic programming problem including the objective function and thestochastic constraints; d) converting the stochastic programming probleminto an equivalent determinate programming problem on condition of thepredetermined probability distribution; and e) solving the determinateprogramming problem to determine capacities of the nodes and the linksso that the objective function is minimized.
 38. The recording mediumaccording to claim 37, wherein the step c) comprises the steps of:generating a stochastic path accommodation constraint for causing therequested capacity of the demand to be accommodated in the pathcandidates; generating a link accommodation constraint for causingcapacities assigned to path candidates to be accommodated in the links;and generating a stochastic node accommodation constraint for causing atotal of capacities of path candidates passing through a node to beaccommodated in the node.
 39. The recording medium according to claim38, wherein the stochastic path accommodation constraint causes aprobability that a total of capacities assigned to path candidates of ademand is not smaller than the requested capacity of the demand to be atleast a predetermined path accommodation probability, the linkaccommodation constraint causes a total of capacities of path candidatespassing through a link to be accommodated in the link, and thestochastic node accommodation constraint causes a probability that acapacity assigned to a node exceeds a total of termination capacity of alink and termination capacity of the demand to be at least apredetermined node accommodation probability.
 40. The recording mediumaccording to claim 37, wherein the step c) comprises the steps of:generating a path accommodation constraint for causing the requestedcapacity of the demand to be accommodated in the path candidates;generating a stochastic link accommodation constraint for causingcapacities assigned to path candidates to be accommodated in the links;and generating a stochastic node accommodation constraint for causing atotal of capacities of path candidates passing through a node to beaccommodated in the node.
 41. The recording medium according to claim40, wherein, the path accommodation constraint causes a total of ratiosof capacities assigned to path candidates of a demand to be at least 1when it is assumed that the requested capacity of the demand is 1, thestochastic link accommodation constraint causes a probability that acapacity of a link exceeds the total of capacities of path candidatespassing through the link to be at least a predetermined linkaccommodation probability, and the stochastic node accommodationconstraint causes a probability that a node capacity exceeds a total oftermination capacity of a link and termination capacity of the demand tobe at least a predetermined node accommodation probability.
 42. Therecording medium according to claim 40, wherein, the path accommodationconstraint causes a total of capacities assigned to path candidates of ademand to be at least the requested capacity of the demand, thestochastic link accommodation constraint causes a probability that acapacity of a link exceeds a total of capacities of paths passingthrough the link to be at least a predetermined link accommodationprobability, and the stochastic node accommodation constraint causes aprobability that a node capacity exceeds a total of termination capacityof a link and termination capacity of the demand to be at least apredetermined node accommodation probability.
 43. The recording mediumaccording to claim 38, wherein, the stochastic path accommodationconstraint causes a probability that a total of capacities assigned topath candidates of a demand in a network state is not smaller than therequested capacity of the demand to be at least a predetermined pathaccommodation probability, wherein the network state indicates one of anormal state and fault states for some link, the link accommodationconstraint causes a total of capacities of path candidates passingthrough a link in the network state to be accommodated in the link, andthe stochastic node accommodation constraint causes a probability that acapacity assigned to a node exceeds a total of termination capacity of alink and termination capacity of the demand to be at least apredetermined node accommodation probability.
 44. The recording mediumaccording to claim 40, wherein, the path accommodation constraint causesa total of ratios of capacities assigned to path candidates of a demandto be at least 1 when it is assumed that the requested capacity of thedemand is 1, the stochastic link accommodation constraint causes aprobability that a capacity of a link exceeds the total of capacities ofpath candidates passing through the link in a network state to be atleast a predetermined link accommodation probability, wherein thenetwork state indicates one of a normal state and fault states for somelink, and the stochastic node accommodation constraint causes aprobability that a node capacity exceeds a total of termination capacityof a link and termination capacity of the demand to be at least apredetermined node accommodation probability.
 45. The recording mediumaccording to claim 40, wherein, the path accommodation constraint causesa total of capacities assigned to path candidates of a demand in anetwork state to be at least the requested capacity of the demand,wherein indicates one of a normal state and fault states for some link,the stochastic link accommodation constraint causes a probability that acapacity of a link exceeds a total of capacities of paths passingthrough the link in the network state to be at least a predeterminedlink accommodation probability, and the stochastic node accommodationconstraint causes a probability that a node capacity exceeds a total oftermination capacity of a link and termination capacity of the demand tobe at least a predetermined node accommodation probability.